
#1
Jan3013, 10:14 PM

P: 376

if I define The plane: ##F = ℝ## x ##ℝ = \{ (a, b)  a, b ∈ ℝ \} ##
and define addition and multiplication as: (a, b) + (c, d) := (a + c, b + d) (a, b) · (c, d) := (ac, bd) Then ##F## is a field. right? would the multiplication as described here make ℂ a field? 



#2
Jan3013, 11:54 PM

Sci Advisor
P: 778





#3
Jan3113, 12:21 AM

P: 376





#4
Jan3113, 09:46 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,885

Field if I define The plane
Yes, neither (7, 0) nor (0, 8) is the additive identity but neither has a mulitplicative inverse.




#5
Jan3113, 11:35 AM

P: 376

thanks. Basically ℂ will fail to be an integral domain in the first place under this operation.



Register to reply 
Related Discussions  
How to define the b.c.s for the EM field of a perfectly contucting surface?  Classical Physics  1  
Derive electric field of infinite plane from field of infinite line  Introductory Physics Homework  8  
E field above a plane  Introductory Physics Homework  2  
Electric field of a plane  Introductory Physics Homework  4 